Poisson's ratio (v), named after Simeon Poisson, is the ratio of the relative contraction strain, or transverse strain (normal to the applied load), divided by the relative extension strain, or axial strain (in the direction of the applied load). Some materials, called auxetic materials, have a negative Poisson's ratio (NPR). If such materials are stretched (or compressed) in one direction, they become thicker (or thinner) in perpendicular directions.
NPR structures can react differently under applied loads. FIG. 1 illustrates a reactive shrinking mechanism, obtained through a topology optimization process. The unique property of this structure is that it will shrink in two directions if compressed in one direction. FIG. 1 illustrates that when the structure is under a compressive load on the top of the structure, more material is gathered together under the load so that the structure becomes stiffer and stronger in the local area to resist against the load.
FIG. 2 illustrates a negative Poisson's ratio (NPR) structure having the unique property that it will shrink along all directions when compressed in one direction. A nonlinear finite element method has been developed with a multi-step linearized analysis method to predict nonlinear behavior of this material. Effective material properties, such as Young's modulus, Poisson's ratio, material density, and load-bearing efficiency can then be calculated with consideration of the geometric nonlinear effect for any large load amplitudes.
The two-dimensional structures of FIGS. 1 and 2 are composed of a plurality of nested “V-type” unit cells, each unit cell comprising a pair of side points A and B defining a width, 1, a first pair of straight or curved members 202 with constant or variable cross section interconnecting points A and B and intersecting at a point C forming a first V shape defining the “tensile” material, a second pair of straight or curved members 204 with constant or variable cross section interconnecting points A and B and intersecting at a point D forming a second V shape defining the “staffer” material. The unit cells are then connected in rows with the point B of one cell being connected to point A of an adjoining cell until completing a band of unit cells, the unit cells being further connected in stacked columns with the point D of one cell being connected to point C of an adjoining cell.
FIG. 3A illustrates the structure of FIG. 2 with Θ1=60° and Θ2=120°, and FIG. 3B illustrates the structure of FIG. 2 with Θ1=30° and Θ2=60°. FIG. 3 also illustrates the predicted deformation shapes and effective material properties of the two designs, in which, v denotes the effective Poisson's ratio and E is the effective Young's modulus. In FIGS. 3A and B, dashed lines represent the undeformed shape, and solid lines represent the deformed shape. Comparing FIGS. 3A and B, it is seen that the deformation shapes of the two designs are very different under the same loading condition. The effective Poisson's ratio changed from v=−0.96 to v=−7.4 from design #1 to design #2, while the effective Young's modulus changed from E=1.4e3 MPa to E=2.7e3 MPa. This suggests that the second design is better suited to problems that require a large absolute value of NPR and a higher Young's modulus.
FIG. 4 illustrates what happens when localized pressure is applied to an NPR structure. The original structure configuration is shown in dashed lines, and solid lines illustrate the deformed structure obtained from the simulation. As shown in the Figure, the surrounding material is concentrated into the local area due to the negative Poisson's ratio effect as the force is applied. Therefore the material becomes stiffer and stronger in the local area.
NPR materials have attracted significant interest due to their unique behaviors. Unlike conventional materials, a NPR material may shrink when compressed along a perpendicular direction. One result of this behavior is that the material can concentrate itself under the compressive load to better resist the load. Thus, a NPR material becomes stiffer and stronger as the amplitude of the load increases. It has also been found that NPR can improve material/structural properties, including enhanced thermal/shock resistance, fracture toughness, indentation resistance and shear modulus.
Auxetic and NPR structures have been used in a variety of applications. According to U.S. Pat. No. 7,160,621, an automotive energy absorber comprises a plurality of auxetic structures wherein the auxetic structures are of size greater than about 1 mm. The article also comprises at least one cell boundary that is structurally coupled to the auxetic structures. The cell boundary is configured to resist a deformation of the auxetic structures.
There are many other energy absorbing and/or vibration dampening devices, in vehicles and elsewhere, including bushings and joust bumpers. Bushings are particularly important in that they are widely prevalent in chassis and suspension systems. FIG. 5A illustrates typical bushing locations in a vehicular suspension system, and FIG. 5B illustrates typical bushing locations in a vehicle chassis.
The advantages of bushings are many: they connect parts with needed compliance; providing isolation from high frequency shock and jolts of the road; dampen the vibration energy transmitted through the bushing, and reduce noise. Disadvantages of current bushings include the following: they may adversely affect a vehicle's handling and steering characteristics; loss of camber control; front deflection steer; rear deflection and torque steer, and they may adversely affect accuracy of the dynamic simulation.
The vast majority of existing bushings are made of rubber, urethane or nylon, each being a nonlinear viscoelastic material that exhibits displacement-dependent stiffness, relaxation under constant load, and hysteresis response. The force-displacement relationship is nonlinear, frequency dependent, and loading history dependent. Rubber bushings are inexpensive to manufacture. While they provide decent isolation, the larger deflection may adversely affect handling and steering characteristics. Urethane bushings are harder and provide less deflection and better handling and steering performance. However, urethane bushings offer little ability to absorb rotational shear. Nylon bushings and inserts are relatively inexpensive, but require sleeves machined to tight tolerances.